{To be on a high horse}, to be on one's dignity; to bear
one's self loftily. [Colloq.]

{With a high hand}.
(a) With power; in force; triumphantly. ``The children of
Israel went out with a high hand.'' --Ex. xiv. 8.
(b) In an overbearing manner, arbitrarily. ``They governed
the city with a high hand.'' --Jowett (Thucyd. ).